Math + Travel = Unique Course

by by Rob Cooley, assistant professor of anthropology and environmental science. Photos by Rob Cooley, except as credited.

Something unusual is afoot in the classroom where Curt Vander Vere and I are conducting a new course, Introduction to Non-European Mathematics. If the title alone doesn't give it away, this course is a unique blend of mathematics, anthropology and international cultural experiences that provides a new and exciting opportunity for Pennsylvania College of Technology students.

MTH 155 and 156 is a survey of mathematical concepts developed by non-European cultures – Egyptian, Babylonian, African, Chinese and, in particular, those of native Central and South American civilizations. The classroom experience explores their mathematics by studying examples taken from their architecture, astronomy, art and other cultural components.

... the course is not "just" mathematics. It is an attempt to show that the modern world is a complex mixture of unique cultures ...

However, the course is not "just" mathematics. It is an attempt to show that the modern world is a complex mixture of unique cultures, with a diversity of perspectives about the world. The course emphasizes and demonstrates through the travel experience that many of these different cultural systems remain in use by modern peoples today. Consequently, the course is centered around a structured, firsthand cultural field experience with a group that still utilizes non-European systems of mathematics – the Maya.

The field-experience part of the course has two goals. First, it gives the students an opportunity to observe a modern culture that still practices the mathematical principles learned in the classroom part of the course. Second, it gives them a true international travel experience, emphasizing the difference between a tourist and a traveler, requiring them to step outside their cultural comfort zone. The students kept ethnographic travel journals during their trip to help them process their experience and take their travels beyond tourism. The goal was to enable the students to focus and help them have as deep a cultural experience as possible during their travels. The job market is increasingly global, and an international experience such as this expands students' cultural perspectives and truly gives them a deeper appreciation of cultural diversity.

The trip itinerary was designed for Penn College by the Maya Exploration Center, a nonprofit organization dedicated to the study of ancient Mayan civilization. The MEC specializes in providing educational tours and studies of ancient Mayan science. In particular, the MEC, through its study abroad programs, helps students understand the ancient ruins and celebrate the modern Maya and appreciate them as the descendents of one of the world's great early civilizations.

The group left Williamsport on the evening of Dec. 27 and returned early in the morning of Jan. 5. Accompanying Vander Vere and I were students Dawn Bletz, Matt Cox, Matt Druckenmiller, Mat Johnson, Laurie Kiss (an instructor of mathematics who took the course as a nondegree student), Ryan McDonald, Jason Paris and Wayne Roush.

Mayan Mathematics

Archaeological studies of the glyphs carved by Maya onto rock stelae, artfully drawn on paper codices, painted on pottery and other graphical work that remains, definitively show how sophisticated their culture was. Decades of research has generated a detailed understanding of the Mayan calendar system, their astronomical understandings and their interactions with neighboring contemporary groups.

In particular, scholars have determined that the Maya developed a very sophisticated mathematical system that was elegant in its simplicity of graphical symbols (see illustration) but also very powerful – some ancient glyphs have been interpreted as showing Maya using calculations to generate sums greater than millions!

The Maya utilized a base-20 numeral system to structure their mathematical inquiries, and even independently invented the concept of zero. (Archaeologists estimate this occurred between 2000 B.C. and A.D. 300.)

The group arrived and went first to Guatemala City, where we were met by Christopher Powell, our MEC archaeologist and guide, a fascinating and accomplished archaeologist who has dedicated his career to the study of ancient Mayan culture. His decades of experience provided a deep and colorful narrative of adventure, discovery, and history as he guided the group through three of the major Mayan cultural sites and across the Guatemalan landscape.

The experience began the day we arrived in the country: That afternoon, the students visited a small museum focused on the Mayan history of Guatemala City. The next day, they visited the National Anthropology Museum and viewed an extensive collection of art, jade carvings, ceramics, stone sculptures, glyphs and more that spanned the representative periods of the Mayan culture. That afternoon, the group flew to the small city of Flores, 200 miles northwest of Guatemala City, situated in the northern lowlands surrounding Lake PetÚn Itza. From there, the group visited three of the major archaeological sites in the country: Tikal, Yaxcha and Seibal.

Powell provided fascinating evening lectures that tied the archaeological sites visited to mathematical and cultural topics, including ancient Mayan history, geometry and astronomy. Under his guidance, the students visited rain forests, traveled across lakes and down rivers, and climbed countless temples. On New Year's Day, the students rose at 4 in the morning, hiked through the darkness and climbed one of the largest temples in Tikal to experience daybreak as the sun illuminated the temples and forest canopy. The students enjoyed learning the language, trying new Mayan foods, negotiating with vendors in street markets, observing wildlife and mastering how to negotiate international airports.

After their return, the students began work on class projects that they presented later in the spring semester.

The Fall 2011 class will travel to Mexico's Yucatan Peninsula, staying in the charming city of Merida and studying some of the region's archaeological treasures. Sites to be visited will include Dzibilchaltun, the longest continually occupied city in the Mayan world; Chichen Itza; Mayapan; and Uxmal. To learn more about this or other study abroad programs, contact Shanin L. Dougherty, international programs specialist. ■

One of the Great Early Civilizations

The Maya were an agricultural, preindustrial culture and depended heavily on an intimate understanding of the environment, seasons and the passage of time. It seems no coincidence that they developed an elegant and highly precise system of astronomy. It is frequently noted by Mayan scholars that ancient Mayan astronomical charts of the lunar cycle and the planets are equal to or better than any other civilization that did not utilize modern instruments to aid their observations.

The Maya generated an accurate measurement of the solar year and used an annual calendar that measured 365 days. They even accounted for the inaccuracy of this calendar and incorporated adjustments to keep it accurate at regular intervals. The Mayan calendar incorporated both the lunar cycle (haab) and the agricultural cycle (tzolkin). That way, each day had both astronomical as well as agricultural significance, and as such, some days were more significant and auspicious for events, such as planting, than others.

Mayan tourists from Guatamala traveling to see the sacred ancient Mayan sites in Tikal.

McDonald during a boat trip from Flores to ancient ruins in Seibal.

The group approaches one of the few round Mayan structures, believed to be an astronomical observatory. The site is in Seibal.

The students take notes in their journals as archaeologist and host Chris Powell tells them about the ancient city of Seibal.

Rob Cooley, department head, Social Sciences and Humanities, is also an assistant professor of anthropology and environmental science in the School of Integrated Studies. Cooley holds a doctorate in ecological anthropology from the University of Georgia and a bachelor's degree in biology from Bucknell University. He has been with Penn College since 2003.